Is there a "percentage fallacy"?

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A couple years ago, Aaron Swartz blogged about what he called the "percentage fallacy":

There’s one bit of irrationality that seems like it ought to be in behavioral economics introduction but mysteriously isn’t. For lack of a better term, let’s call it the percentage fallacy. The idea is simple:

One day I find I need a blender. I see a particularly nice one at the store for $40, so I purchase it and head home. But on the way home, I see the exact same blender on sale at a different store for $20. Now I feel ripped off, so I drive back to the first store, return the blender, drive back to the second store, and buy it for $20.

The next day I find I need a laptop. I see a particularly nice one at the store for $2500, so I purchase it and head home. But on the way home, I see the exact same laptop for $2480. “Pff, well, it’s only $20,” I say, and continue home with the original laptop.

I’m sure all of you have done something similar — maybe the issue wasn’t having to return something, but spending more time looking for a cheaper model, or fiddling with coupons and rebates, or buying something of inferior quality. But the basic point is consistent: we’ll do things to save 50% that we’d never do to save 1%.

He recently followed up with a speculation that this may explain some irrational behaviour normally attributed to hyperbolic discounting:

In a famous experiment, some people are asked to choose between $100 today or $120 tomorrow. Many choose the first. Meanwhile, some people are asked to choose between $100 sixty days from now or $120 sixty-one days from now. Almost everyone choose the laster. The puzzle is this: why are people willing to sacrifice $20 to avoid waiting a day right now but not in the future?

The standard explanation is hyperbolic discounting: humans tend to weigh immediate effects much more strongly than distant ones. But I think the actual psychological effect at work here is just the percentage fallacy. If I ask for the money now, I may have to wait 60 seconds. But if I get it tomorrow I have to wait 143900% more. By contrast, waiting 61 days is only 1.6% worse than waiting 6 days. Why not wait an extra 2% when you get 16% more money for it?

Has anyone done a test confirming the percentage fallacy? A good test would be to show people treat the $100 vs. $120 tradeoff as equivalent to the $1000 to $1200 tradeoff.

Is this a real thing? Is there any such research? Is there existing evidence that does especially support the usual hyperbolic discounting explanation over this?

A couple years ago, Aaron Swartz blogged about what he called the "percentage fallacy":

There’s one bit of irrationality that seems like it ought to be in behavioral economics introduction but mysteriously isn’t. For lack of a better term, let’s call it the percentage fallacy. The idea is simple:

One day I find I need a blender. I see a particularly nice one at the store for $40, so I purchase it and head home. But on the way home, I see the exact same blender on sale at a different store for $20. Now I feel ripped off, so I drive back to the first store, return the blender, drive back to the second store, and buy it for $20.

The next day I find I need a laptop. I see a particularly nice one at the store for $2500, so I purchase it and head home. But on the way home, I see the exact same laptop for $2480. “Pff, well, it’s only $20,” I say, and continue home with the original laptop.

I’m sure all of you have done something similar — maybe the issue wasn’t having to return something, but spending more time looking for a cheaper model, or fiddling with coupons and rebates, or buying something of inferior quality. But the basic point is consistent: we’ll do things to save 50% that we’d never do to save 1%.

He recently followed up with a speculation that this may explain some irrational behaviour normally attributed to hyperbolic discounting:

In a famous experiment, some people are asked to choose between $100 today or $120 tomorrow. Many choose the first. Meanwhile, some people are asked to choose between $100 sixty days from now or $120 sixty-one days from now. Almost everyone choose the laster. The puzzle is this: why are people willing to sacrifice $20 to avoid waiting a day right now but not in the future?

The standard explanation is hyperbolic discounting: humans tend to weigh immediate effects much more strongly than distant ones. But I think the actual psychological effect at work here is just the percentage fallacy. If I ask for the money now, I may have to wait 60 seconds. But if I get it tomorrow I have to wait 143900% more. By contrast, waiting 61 days is only 1.6% worse than waiting 6 days. Why not wait an extra 2% when you get 16% more money for it?

Has anyone done a test confirming the percentage fallacy? A good test would be to show people treat the $100 vs. $120 tradeoff as equivalent to the $1000 to $1200 tradeoff.

Is this a real thing? Is there any such research? Is there existing evidence that does especially support the usual hyperbolic discounting explanation over this?

Expressing probabilities as percents gets a bit weird, because subtraction doesn't really work like it should. I don't understand. The expected value is what you'd get by straight subtraction.

Are you implying that the difference between 2% and 3% should be 1 in 50-33=17, or 5.9%? In that case, the difference between 100% and 99.99999% would be 100%, when they're really almost exactly the same.